General Relativity: An Introduction for Physicists · Problem 15.27

Cosmological models — Hobson, Efstathiou & Lasenby

Physics · mattig-formula-luminosity-distance

Problem

For a dust-only Friedmann model, show that the luminosity--distance relation varies with redshift as dL(z)=2cH0Ωm,02[Ωm,0 z+(Ωm,0−2)(Ωm,0 z+1−1)].d_L(z) = \frac{2c}{H_0\Omega_{\mathrm{m},0}^2}\left[\Omega_{\mathrm{m},0}\, z + (\Omega_{\mathrm{m},0}-2)\left(\sqrt{\Omega_{\mathrm{m},0}\, z+1}-1\right)\right]. This result is known as Mattig's formula.

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